Quantum sensing of high-frequency gravitational waves with ion crystals

TL;DR

This work proposes a tabletop method to detect high-frequency gravitational waves using two-dimensional ion crystals in a Penning trap. Gravitational waves resonantly excite parity-odd drumhead modes, read out via a optical-dipole-force–driven spin readout, enabling quantum-enhanced sensitivity via spin squeezing. The analysis derives mode couplings, resonance conditions, noise models, and parameter optimizations, showing sensitivity improves with larger N and crystal radius and extends over 10 kHz–10 MHz. The approach offers a distinctive GW signature through parity-selective coupling and may approach or exceed the reach of other high-frequency GW experiments, with future directions including 3D crystals, center-of-mass mode detection, and graviton-photon conversion.

Abstract

A detection method for high-frequency gravitational waves using two-dimensional ion crystals is investigated. Gravitational waves can resonantly excite the drumhead modes of the ion crystal, particularly the parity-odd modes. In the optical dipole force protocol, entanglement between the drumhead modes and the collective spins transfers the excitation of the drumhead modes to the rotation of the total spin. Furthermore, gravitational wave detection beyond the standard quantum limit becomes possible as a squeezed spin state is generated through this entanglement. The sensitivity gets better with a larger ions crystals as well as a larger number of the ions. Future realization of large ion crystals can significantly improve the sensitivity to gravitational waves in the 10 kHz to 10 MHz region.

Figures (3)

• Figure 1: Schematic illustration of the Ramsey-type experimental sequence for the detection of external fields, such as gravitational waves. The sequence consists of state preparation, an ODF pulse of duration $\tau$, free evolution under a gravitational wave for a time $T$, an inverse ODF pulse, and final spin detection.
• Figure 2: Sensitivities to the amplitude of gravitational waves, $h_0$, as a function of the frequency $f$ are shown. Cyan, blue, and black colored lines correspond to ion numbers of $N=150$, $10^5$, $10^8$, respectively. The solid curves represent the achievable sensitivity with one-year observation for each frequency bin, while the dotted curves show the sensitivities obtained by scanning the entire frequency range during the total observation time of one year. The single measurement time $T$ and the ODF duration $\tau$ are chosen to optimize the sensitivities as $(T, \tau) = (0.04~{\rm s}, 0.3~{\rm ms})$, $(0.08~{\rm s}, 1~{\rm ms})$, and $(0.1~{\rm s}, 3~{\rm ms})$ for $N=150$, $10^5$, and $10^8$, respectively.
• Figure 3: Sensitivities to the noise-equivalent spectral density of gravitational waves, $S_h^{\rm noise}(f)$, as a function of the frequency $f$ are shown. The experimental parameters are the same as Fig. \ref{['figh0odd']}. The pink band and the red line express the existing experiments, the Fermilab Holometer Holometer:2016qoh and the Bulk Acoustic Wave (BAW) experiments Goryachev:2014yra.